Choose the best definition for each.
(1) Newton's First Law (2) Newton's Second Law
(3) Newton's Second Law (4) Stable Position of a mechanical system
(5) Hooke's Law for Springs (6) Restoring Force in a mechanical system
(7) Potential Energy of a mechanical system (8) Kinetic Energy of a mechanical system
(9) Natural Frequency of a mechanical system (10) Resonance of a mechanical system
From these definitions
(A) a body remains at rest or in motion with a constant velocity unless acted upon by an external force.
(B) a heavier object will fall more quickly than a lighter object.
(C) the rate of change of momentum is proportional to the imposed force and goes in the direction of the force.
(D) a periodic motion in which the displacement is symmetrical about a point
(E) the configuration in which a system comes to rest
(F) mechanical energy that a body has by virtue of its motion
(G) the specific frequency at which a system started into motion vibrates
(H) stored energy that a body has by virtue of its position
(I) the principle that the change in size of a solid is proportional to the force applied to it
(J) a force always directed towards the stable position.
(K) action and reaction are equal and opposite.
Section II: Understanding
The following question groups all concern mechanical systems of a mass and some kind of a restoring force:
Questions 1, 2 and 3 concern a certain pendulum, which takes one second per complete swing.
Questions 4, 5 and 6 concern a certain mass and spring system, which takes one second per complete bounce.
In each question, we consider the effect of changing only one of the properties of the original system, asking, now how long will the time be for each cycle?
For each of these questions, choose the closest correct answer from these choices:
A - 0.5 sec
B - 0.71 sec
C - 1 sec
D - 1.41 sec
E - 2 sec
Questions 1, 2 and 3 concern a certain pendulum, which takes one second per complete swing.
(1) Keep the original weight, but make the supporting string twice as long. Now how long will the time be for each swing?
(2) Keep the original supporting string, but make the weight twice as heavy. Now how long will the time be for each swing? (3) We start this pendulum swinging through a distance of two inches to either side, but after awhile, due to friction, it is swinging only one inch to either side. Now how long will the time be for each swing?
Questions 4, 5 and 6 concern a certain mass and spring system, which takes one second per complete bounce.
(4) Keep the original weight, but make the supporting spring twice as stiff, so that a given force only moves it half as far. Now how long will the time be for each bounce? (5) Keep the original supporting spring, but make the weight twice as heavy. Now how long will the time be for each bounce?
(6) We start this weight moving through a vertical distance of two inches above and below the stable point, but after awhile, due to friction, it is moving only one inch above and below the stable point. Now how long will the time be for each bounce?
Section III: Application
1.What is a simple harmonic motion? State its characteristics.
2.For a particle in linear simple harmonic motion ,the average kinetic energy over a period of oscillation, equals the average potential energy over the same period. Why?
3.Why are longitudinal waves also called pressure waves?
4.Transverse waves are not formed in liquids and gases why?
5.Distinguish between free, forced, and resonant oscillation with drawn illustrations.
6.What is a spring constant?
7. Find (and explain) the spring constant value in case of two identical springs with constant K connected in
(i)series,
(ii) parallel.
8.What are fundamental note and overtones? What are harmonics?
9.Briefly explain the terms wavelength, frequency, time period and velocity of wave motion. Establish relation between them.
10.Explain some significant properties of wave motion.
11.State and explain superposition of waves.
12.What are standing, or stationary, waves?
Section I: Definitions
Choose the best definition for each.(1) Newton's First Law
(2) Newton's Second Law
(3) Newton's Second Law
(4) Stable Position of a mechanical system
(5) Hooke's Law for Springs
(6) Restoring Force in a mechanical system
(7) Potential Energy of a mechanical system
(8) Kinetic Energy of a mechanical system
(9) Natural Frequency of a mechanical system
(10) Resonance of a mechanical system
From these definitions
(A) a body remains at rest or in motion with a constant velocity unless acted upon by an external force.
(B) a heavier object will fall more quickly than a lighter object.
(C) the rate of change of momentum is proportional to the imposed force and goes in the direction of the force.
(D) a periodic motion in which the displacement is symmetrical about a point
(E) the configuration in which a system comes to rest
(F) mechanical energy that a body has by virtue of its motion
(G) the specific frequency at which a system started into motion vibrates
(H) stored energy that a body has by virtue of its position
(I) the principle that the change in size of a solid is proportional to the force applied to it
(J) a force always directed towards the stable position.
(K) action and reaction are equal and opposite.
Section II: Understanding
The following question groups all concern mechanical systems of a mass and some kind of a restoring force:
Questions 1, 2 and 3 concern a certain pendulum, which takes one second per complete swing.
Questions 4, 5 and 6 concern a certain mass and spring system, which takes one second per complete bounce.
In each question, we consider the effect of changing only one of the properties of the original system, asking, now how long will the time be for each cycle?
For each of these questions, choose the closest correct answer from these choices:
A - 0.5 sec
B - 0.71 sec
C - 1 sec
D - 1.41 sec
E - 2 sec
Questions 1, 2 and 3 concern a certain pendulum, which takes one second per complete swing.
(1) Keep the original weight, but make the supporting string twice as long. Now how long will the time be for each swing?
(2) Keep the original supporting string, but make the weight twice as heavy. Now how long will the time be for each swing?
(3) We start this pendulum swinging through a distance of two inches to either side, but after awhile, due to friction, it is swinging only one inch to either side. Now how long will the time be for each swing?
Questions 4, 5 and 6 concern a certain mass and spring system, which takes one second per complete bounce.
(4) Keep the original weight, but make the supporting spring twice as stiff, so that a given force only moves it half as far. Now how long will the time be for each bounce?
(5) Keep the original supporting spring, but make the weight twice as heavy. Now how long will the time be for each bounce?
(6) We start this weight moving through a vertical distance of two inches above and below the stable point, but after awhile, due to friction, it is moving only one inch above and below the stable point. Now how long will the time be for each bounce?
Section III: Application
1.What is a simple harmonic motion? State its characteristics.
2.For a particle in linear simple harmonic motion ,the average kinetic energy over a period of oscillation, equals the average potential energy over the same period. Why?
3.Why are longitudinal waves also called pressure waves?
4.Transverse waves are not formed in liquids and gases why?
5.Distinguish between free, forced, and resonant oscillation with drawn illustrations.
6.What is a spring constant?
7. Find (and explain) the spring constant value in case of two identical springs with constant K connected in
(i)series,
(ii) parallel.
8.What are fundamental note and overtones? What are harmonics?
9.Briefly explain the terms wavelength, frequency, time period and velocity of wave motion. Establish relation between them.
10.Explain some significant properties of wave motion.
11.State and explain superposition of waves.
12.What are standing, or stationary, waves?